Sill intrusions with a characteristic saucer shape are observed in many sedimentary basins worldwide. Previous models of their emplacement usually assume a purely elastic host-rock rheology. However, a growing number of field observations show a non-negligible amount of faulting and associated plastic deformation related to their emplacement. We use a rigid-plasticity approach to study the conditions for nonelastic deformation and the damage patterns related to sill emplacement. The results show that the characteristic saucer shape is ubiquitously reproduced using this approach. By varying the sill diameter, we observe that the shape of the damage zones changes from straight for small diameters to curved for large ones. The overpressure of the sill is seen to decrease rapidly with increasing sill diameter, suggesting that longer sills are more prone to undergoing plastic deformation. In contrast to previous studies, which assume that an asymmetric stress field deflects the propagating sill tip, our models suggest that saucer-shaped sills are created due to shear failure caused by an inflating flat sill. This implies that plastic damage is a precursor for the emplacement of saucer-shaped sills.